In which quadrant does ø lie if the following statements are true sec ø < 0 and csc ø > 0

Ф lies in the 2nd quadrant

Step-by-step explanation:

1. If angle Ф lies in the 1st quadrant, then

2. If angle Ф lies in the 2nd quadrant, then

3.If angle Ф lies in the 3rd quadrant, then

4. If angle Ф lies in the 4th quadrant, then

∵ sec Ф < 0

∴ sec Ф is a negative value

∵ cos Ф = 1/sec Ф

∴ cos Ф is a negative value

∵ csc Ф > 0

∴ csc Ф is a positive value

∵ sin Ф = 1/csc Ф

∴ sin Ф is a positive value

→ By using the second rule above

∴ Ф lies in the 2nd quadrant

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: